Heesch Weyl Fermions in inadmissible chiral antiferromagnets

Symmetry is a crucial factor in determining the topological properties of materials. In nonmagnetic chiral crystals, the existence of the Kramers Weyl fermions reveals the topological nature of the Kramers degeneracy at time-reversal-invariant momenta (TRIMs). However, it is not clear whether Weyl nodes can also be pinned at points of symmetry in magnetic materials where the time-reversal is spontaneously broken. In this study, we introduce a new type of Weyl fermions, called Heesch Weyl fermions (HWFs), which are stabilized and pinned at points of symmetry by the Heesch groups in inadmissible chiral antiferromagnets. The emergence of HWFs is fundamentally different from that of Kramers Weyl fermions, as it does not rely on any anti-unitary symmetry $\mathcal{A}$ that satisfies $\mathcal{A}^2=-1$. Importantly, the emergence of HWFs is closely related to the antiferromagnetic order, as they are generally obscured by nodal lines in the parent nonmagnetic state. Using group theory analysis, we classify all the magnetic little co-groups of momenta where Heesch Weyl nodes are enforced and pinned by symmetry. With the guidance of this classification and first-principles calculations, we identify antiferromagnetic (AFM) materials such as YMnO$_3$ and Mn$_3$IrGe as candidate hosts for the AFM-order-induced HWFs.We also explore novel properties of Heesch Weyl antiferromagnets, such as nonlinear anomalous Hall effects and axial movement of Heesch Weyl nodes. Our findings shed new light on the role of symmetry in determining and stabilizing topological properties in magnetic materials, and open up new avenues for the design and exploration of topological materials.